Conservative MP Geoffrey Clifton-Brown, who was among nine Tories who met the prime minister with their concerns over the issue this week, said the proposals would not pass the Commons in their present form. At least a dozen backbenchers also confronted Greening about the proposals at a meeting of the 1922 committee on Wednesday night.

Of the top 50 Tory-held marginal seats, 18 have more schools losing out on funding than gaining. The seats include Crewe and Nantwich, the seat of education minister Ed Timpson, and Brighton Kemptown, where treasury minister Simon Kirby sits.

The threat of a revolt comes after a report found all schools in England were likely to face real-term cuts to funding by 2019-20, with about half facing a reduction per pupil of 6-11%, in line with the government’s proposed funding formula.

The Education Policy Institute research found that even those schools which the government has said would benefit under the new formula would be worse off. This was as a result of inflation, coupled with a reduction in local authority funding and the £3bn of education savings that schools must make by 2019-20.

Clifton-Brown, who said he had never voted against the government in 25 years in parliament, said there had been hints that the government was reconsidering the formula. “I think ministers recognise, and indeed I told Justine Greening in a later meeting, that this wouldn’t go through in its present form,” he told BBC Radio 4’s Today programme.

He said the prime minister and the education secretary were “listening to what responses they get back” from the consultation. “I think knowing that they will have difficulty getting it through the house, they will have to alter it.”

Schools in his constituency, the Cotswolds in Gloucestershire, had “pared everything to the bone” in recent years, the MP said. “Under this new formula, all my large primaries and all of my secondaries will actually see a cash cut in their budgets.

“One teacher put it to me that on this basis, on this so-called new fair funding formula, if nothing is done, if he doesn’t make teachers redundant, in three years’ time his teacher salary bill will be 105% of his total income, so he has to make teachers redundant. The result of that is that courses will be merged and education standards will start to drop.”

Osborne told his local paper he met Greening last week to raise the concerns about the impact of the funding formula on Cheshire schools. All 34 schools in his Tatton constituency would end up losing out from the funding formula, in breach of the Conservative manifesto commitment that promised to protect per-pupil funding. Tatton’s pupils would stand to lose around £100 each in funding under the current proposals.

“There’s no substitute to giving the message direct to the education secretary – so that’s what I did,” Osborne said. “Everyone knows we need a new formula and that there isn’t extra money lying around, but the money needs to be fairly distributed. I said when I met with local schools I would be a strong voice for them – and that’s what I will continue to do.”

Angela Rayner MP, the shadow education secretary, said the government needed to listen to its own backbenchers. “The chancellor’s chickens are coming home to roost. Tory MPs are in open revolt, schools across the country are facing cuts and heads are being forced to choose between cutting subjects, staff or school days,” she said.

“Even the former chancellor George Osborne is demanding a rethink, and I’m sure it would make a great campaign for the Evening Standard. So it’s time the PM kept the Tories’ promise to protect school funding for every pupil – before she is forced in to yet another humiliating climbdown.”

The consultation on the funding formula would close next week, a No 10 spokesman said. “It is a genuine consultation and then we will respond,” the prime minister’s spokesman said. “We have protected the schools budget in real terms. We have the highest level of school spending on record. We are honouring our commitments in terms of increasing the education budget.”